Mean of a Joint Random Variable

**Bidski** · 08-23-2012 09:00 PM

I am new to statistics, so bare with me please.
I have the following question to answer.

Suppose X and Y have joint density

$f(x, y) = \left\{ \begin{array}{l l} 3x & \quad 0 \leq x \leq y \leq 1\\ 3y & \quad 0 \leq y \leq x \leq 1\\ 0 & \quad \text{otherwise} \end{array} \right.$

Find the mean of Y.

As I understand it, I need to do the following to find the mean of Y
$\int_{-\infty}^{\infty}\int_{-\infty}^{\infty}yf(x, y)dxdy$

My problem is with the limits of integration. Am I correct to assume that I need to split this double integral up into 2 double integrals and add them together? To this effect I have come up with
$\int_{0}^{1}\int_{0}^{y}3xydxdy + \int_{0}^{1}\int_{0}^{x}3y^{2}dxdy$

Is this what I want to do?

Thanks for your help.

Bidski

**Dason** · 08-23-2012 09:09 PM

Your second integral doesn't quite make sense. If you're integrating with respect to x first then you shouldn't have x as one of your integration limits.

**Bidski** · 08-23-2012 09:50 PM

Oops, sorry. That part is a typo. It should be dydx for the second double integal.

**Dason** · 08-23-2012 10:11 PM

Ah - then it looks good to me.

**Bidski** · 08-23-2012 10:12 PM

Cool, thanks for the confirmation.

Thread: Mean of a Joint Random Variable

Thread Tools

Display

Mean of a Joint Random Variable

Re: Mean of a Joint Random Variable

The Following User Says Thank You to Dason For This Useful Post:

Re: Mean of a Joint Random Variable

Re: Mean of a Joint Random Variable

The Following User Says Thank You to Dason For This Useful Post:

Re: Mean of a Joint Random Variable

Posting Permissions